**TI-84+ and Casio (fx-CG 50) Micropython: Simplifying Nested Radicals**

**Introduction**

The following program will simplifying the following expression:

√(x + y) = √a + √b

The input is x and y, with output a and b. The following conditions are implied: x > y and x > 0.

To see the derivation of simplification and examples, please check out this blog entry:

https://edspi31415.blogspot.com/2018/11/simplifying-nested-radicals.html

**TI 84 Plus Program: DENEST**

"EWS 2018-11-12"

Disp "√(X+Y)=√(A)+√(B)","X>Y","X>0"

Prompt X,Y

X/2+1/2*√(X^2-Y^2)→A

X/2-1/2*√(X^2-Y^2) →B

√(A)→Z

round(Z,9)→Z

Disp " "

If Y<0 font="">

Then

If fPart(Z)=0

Then

Disp √(A),"- √(",B,")"

Else

Disp "√(",A,")- √(",B,")"

End

Else

If fPart(Z)=0

Then

Disp √(A),"+ √(",B,")"

Else

Disp "√(",A,")+ √(",B,")"

End

End

**Casio Micropython (fx-CG 50) Script denest.py**

Input is the form of:

√(x1 * √x2 + y1 * √y2) = √a + √b

import math

print("sqrt(x+y)=")

print("sqrt(a)+sqrt(b)")

print("x>y","x>0")

print(" ")

print("x1*sqrt(x2)")

x1=float(input("x1:"))

x2=float(input("x2:"))

x=x1*math.sqrt(x2)

print(" ")

print("y1*sqrt(y2)")

y1=float(input("y1:"))

y2=float(input("y2:"))

y=y1*math.sqrt(y2)

a=x/2+math.sqrt(x**2-y**2)

b=x/2-math.sqrt(x**2-y**2)

z=math.sqrt(a)

z=round(z,10)

a=round(a,10)

b=round(b,10)

if y<0: font="">

if z-int(z)==0:

print(z,"-sqrt(")

print(b,"?")

else:

print("sqrt(",a)

print("-sqrt(")

print(b,")")

else:

if z-int(z)==0:

print(z,"+sqrt(")

print(b,")")

else:

print("sqrt(",a)

print("+sqrt(")

print(b,")")

Source:

Michael J. Wester, Editor. Computer Algebra Systems: A Practical Guide John Wiley & Sons: Chichester 1999. ISBN 978-0-471-983538

Eddie

All original content copyright, © 2011-2018. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. Please contact the author if you have questions.